Given a segment of length a, show two different ways for constructing a segment of length (i) (square root of (19)) * a and (ii) a * (square root of (2/3))

Oct 30th 2010, 12:40 AM

Opalg

Quote:

Originally Posted by MATNTRNG

Given a segment of length a, show two different ways for constructing a segment of length (i) (square root of (19)) * a and (ii) a * (square root of (2/3))

Start by assembling a checklist of techniques for constructing segments whose length is some multiple of . For example, can you construct one with length (where is a whole number)? What about ? ... or ? What about for other values of ? (Think of a right-angled triangle in which two sides are known multiples of . What will be the length of the hypotenuse?)